About how many members are expected to be between 15 years old and 31 years old?

Question

The ages of members of an online gaming group are normally distributed with a mean of 23 years and a standard deviation of 4 years.

There are 300 members in the group.

Answer 1

Compute the z-scores for x=15 and for x=31:

 

z = (x-μ)/σ

• z = z score
• x = data point = 15 and 31
• μ = mean = 23
• σ = standard deviation = 4

 

Once you have the two z-scores, look up the percentiles on a z-score table (http://www.z-table.com/).  The answer is:

 

300·(Percentile for z of 31 - Percentile for z of 15)